Solve for $x$ and $y$ using elimination. ${5x-6y = -29}$ ${-4x+5y = 25}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $5$ ${20x-24y = -116}$ $-20x+25y = 125$ Add the top and bottom equations together. ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {5x-6y = -29}\thinspace$ to find $x$ ${5x - 6}{(9)}{= -29}$ $5x-54 = -29$ $5x-54{+54} = -29{+54}$ $5x = 25$ $\dfrac{5x}{{5}} = \dfrac{25}{{5}}$ ${x = 5}$ You can also plug ${y = 9}$ into $\thinspace {-4x+5y = 25}\thinspace$ and get the same answer for $x$ : ${-4x + 5}{(9)}{= 25}$ ${x = 5}$